My best friend just sent me a calendar invite for a ski day. We've been friends since we were four and have done everything that entails (cub scouts, sports, boy scouts, roommates, breakups, best-manning, etc.). I wouldn't ever want to lose touch with the guy, but even we schedule things like this. It's just part of lives getting more complicated and prioritizing things that matter.
I think the weird part for me isn't the shared calendar event, but the recurring thing. I'd have no issue if friends started sending me invites for things I agreed to, or with the expectation I might say yes or no..but a recurring thing makes it really awkward when you decide you don't feel like it that month, or want to end it altogether.
You just say you can't make it each time for 2-3 of them, then explain things are just busy and you don't want to keep cancelling so let's remove the recurring event until you've got the time again.
What's awkward about that? It's basically just the standard way to gracefully end anything recurring, whether it's with friends, a unnecessary business meeting, participation in a club, etc.
I do like the experience. Instead of sending an email or text message you send an invite with all the details and location. If it suits the other person that is good or they make a suggestion for different time or place. It saves a lot of “let’s meet again. Oh let’s compare agendas.” And things not happening anymore.